Mathematics

On f-core equivalence with general widespread externalities

Article Abstract:

A study was conducted to examine the f-core equivalence theorem for continuum economies with widespread externalities. Unlike the 1989 work conducted by Hammond et al., the latest study assumed that externalities need not arise from trading activities. In addition, free disposal of divisible goods was not assumed, and that preferences were required only to attain a minimal change in nonsatiation. Results showed only that any f-core allocation yields a compensated Nash-Walrasian equilibrium.

Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with riskless asset

Article Abstract:

Problems of equilibrium in the two period mean-variance capital asset pricing model with riskless asset was studied. Use of a reduced two-dimensional economy showed that adequate conditions for uniqueness of equilibrium may be provided in the context of risk aversion when utilities are additively separable in mean and variance. The study also demonstrated that generically equilibria are determinate.

An extension of Milleron, Mitjushin and Polterovich's result

Article Abstract:

Previous work on the uniqueness of equilibria in finite dimensions are extended to the case of incomplete markets. To this end, a pure exchange economy where agents have 'separable utilities and shares of aggregate endowments' is investigated. It is shown that equilibrium is attained only if utilities are homogeneous or when agents' coefficients of relative risk aversion are less than four.